Question

What is the focus of the parabola given by the equation y = x2 − 2x − 3?

(4,-15/4) (1,4) (1,-4) (1,15/4) (1,-15/4)

Answer 1

nvm someone answered the question

Answer 2

the focus of the parabola is:
`(1,(-15)/(4) )`

Explanation:

we will convert this given equation of the parabola into the general parabola equation of the type
`4a(y-k)=(x-h)^2`

on converting the given equation of the type
`y=x^2-2 x-3` into general equation of parabola we get that
`4×(1)/(4) (y-(-4))=(x-1)^2`

clearly here vertex=(h,k)=(1,-4) and
`a=(1)/(4)`

so focus=(h,k+a)

hence the given parabola has focus:
`(1,(-15)/(4))`